The confined QHO can be used to describe confinement
effects on physical properties of confined systems. Physical
size and shape of the materials strongly affect
the nature, dynamics of the electronic excitations, lattice vibrations,
and dynamics of carriers. For example, in the mesoscopic systems, the
dimension of system is comparable with the coherence length of
carriers and this leads to some new phenomena that they do not
appear in a bulk semiconductor, such as quantum interference
between carrier's motion [1]}. Recent progress in growth
techniques and development of micromachinig technology in
designing mesoscopic systems and nanostructures, have led to
intensive theoretical [2]} and experimental
investigations [3]} on electronic and optical properties
of those systems. The most important point about the nanoscale
structures is that the quantum confinement effects play the
center-stone role. One can even say, in general, that recent
success in nanofabrication technique have resulted in great
interest in various artificial physical systems (quantum dots,
quantum wires and quantum wells) with new phenomena driven by the
quantum confinement. A number of recent experiments have
demonstrated that isolated semiconductor quantum dots are capable
of emitting light [4]}. It becomes possible to combine high-Q
optical microcavities with quantum dot emitters as the active
medium [5]}. Furthermore, there are many theoretical attempts
for understanding the optical and electronic properties of
nanostructures especially semiconductor quantum dots [6]}. On the other hand, a nanostructure
such as quantum dot, is a system that carrier's motion is
confined inside a small region, and during the interaction with other
systems, the generated excitations such as phonons, excitons and
plasmons are confined in small region. In order to describe the physical properties of these
excitations one can consider them as harmonic oscillator.
